The $4$ points plotted below are on the graph of $y=\log_b{x}$. Based only on these $4$ points, plot the $4$ corresponding points that must be on the graph of $y=b^{x}$ by clicking on the graph. Click to add points
Solution: Let's consider the point on $ y = \log_{ b}{ x}$ with coordinates $(D 3, 1 )$. Since $ y = { b}^ x$ is the inverse of $ y = \log_{ b}{ x}$, the point $( 1,D 3)$ is on the graph of $ y = { b}^ x$. In general, if $(D q, p )$ is on $y = \log_{ b}{ x}$, then $( p,D q)$ is on $ y={ b}^ x$. For each point on $y=\log_b{x}$, we just switch the order of its coordinates to get a point on $y=b^x$. So, $y=b^x$ also has points with coordinates $(0, 1)$, $ (2, 9)$, and $(3, 27)$. Given the points that we know are on ${y=\log_b{x}}$, the graph below shows the $4$ points that must be on ${y=b^x}$. The original $4$ points are also plotted for reference. ${4}$ ${8}$ ${12}$ ${16}$ ${20}$ ${24}$ ${28}$ ${4}$ ${8}$ ${12}$ ${16}$ ${20}$ ${24}$ ${28}$ $y$ $x$